qiskit.aqua.operators.gradients.NaturalGradient

class NaturalGradient(grad_method='lin_comb', qfi_method='lin_comb_full', regularization=None, **kwargs)

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Convert an operator expression to the first-order gradient.

Given an ill-posed inverse problem

x = arg min{||Ax-C||^2} (1)

one can use regularization schemes can be used to stabilize the system and find a numerical solution

x_lambda = arg min{||Ax-C||^2 + lambda*R(x)} (2)

where R(x) represents the penalization term.

Parameters

grad_method (Union[str, CircuitGradient]) – The method used to compute the state gradient. Can be either 'param_shift' or 'lin_comb' or 'fin_diff'.
qfi_method (Union[str, CircuitQFI]) – The method used to compute the QFI. Can be either 'lin_comb_full' or 'overlap_block_diag' or 'overlap_diag'.
regularization (Optional[str]) – Use the following regularization with a least square method to solve the underlying system of linear equations Can be either None or 'ridge' or 'lasso' or 'perturb_diag' 'ridge' and 'lasso' use an automatic optimal parameter search If regularization is None but the metric is ill-conditioned or singular then a least square solver is used without regularization
kwargs (dict) – Optional parameters for a CircuitGradient

init

__init__(grad_method='lin_comb', qfi_method='lin_comb_full', regularization=None, **kwargs)

Parameters

grad_method (Union[str, CircuitGradient]) – The method used to compute the state gradient. Can be either 'param_shift' or 'lin_comb' or 'fin_diff'.
qfi_method (Union[str, CircuitQFI]) – The method used to compute the QFI. Can be either 'lin_comb_full' or 'overlap_block_diag' or 'overlap_diag'.
regularization (Optional[str]) – Use the following regularization with a least square method to solve the underlying system of linear equations Can be either None or 'ridge' or 'lasso' or 'perturb_diag' 'ridge' and 'lasso' use an automatic optimal parameter search If regularization is None but the metric is ill-conditioned or singular then a least square solver is used without regularization
kwargs (dict) – Optional parameters for a CircuitGradient

Methods


`__init__`([grad_method, qfi_method, …])	type grad_method`Union`[`str`, `CircuitGradient`]
`convert`(operator[, params])	type operator`OperatorBase`
`gradient_wrapper`(operator, bind_params[, …])	Get a callable function which provides the respective gradient, Hessian or QFI for given parameter values.
`parameter_expression_grad`(param_expr, param)	Get the derivative of a parameter expression w.r.t.

Attributes


`grad_method`	Returns `CircuitGradient`.
`qfi_method`	Returns `CircuitQFI`.
`regularization`	Returns the regularization option.

convert

convert(operator, params=None)

Parameters

operator (OperatorBase) – The operator we are taking the gradient of.
params (Union[ParameterVector, ParameterExpression, List[ParameterExpression], None]) – The parameters we are taking the gradient with respect to.

Return type

OperatorBase

Returns

An operator whose evaluation yields the NaturalGradient.

Raises

TypeError – If operator does not represent an expectation value or the quantum state is not CircuitStateFn.
ValueError – If params contains a parameter not present in operator.

grad_method

Returns CircuitGradient.

Return type

CircuitGradient

Returns

CircuitGradient.

gradient_wrapper

gradient_wrapper(operator, bind_params, grad_params=None, backend=None)

Get a callable function which provides the respective gradient, Hessian or QFI for given parameter values. This callable can be used as gradient function for optimizers.

Parameters

operator (OperatorBase) – The operator for which we want to get the gradient, Hessian or QFI.
bind_params (Union[ParameterExpression, ParameterVector, List[ParameterExpression]]) – The operator parameters to which the parameter values are assigned.
grad_params (Union[ParameterExpression, ParameterVector, List[ParameterExpression], Tuple[ParameterExpression, ParameterExpression], List[Tuple[ParameterExpression, ParameterExpression]], None]) – The parameters with respect to which we are taking the gradient, Hessian or QFI. If grad_params = None, then grad_params = bind_params
backend (Union[BaseBackend, QuantumInstance, None]) – The quantum backend or QuantumInstance to use to evaluate the gradient, Hessian or QFI.

Returns

Function to compute a gradient, Hessian or QFI. The function takes an iterable as argument which holds the parameter values.

Return type

callable(param_values)

parameter_expression_grad

static parameter_expression_grad(param_expr, param)

Get the derivative of a parameter expression w.r.t. the given parameter.

Parameters

param_expr (ParameterExpression) – The Parameter Expression for which we compute the derivative
param (ParameterExpression) – Parameter w.r.t. which we want to take the derivative

Return type

Union[ParameterExpression, float]

Returns

ParameterExpression representing the gradient of param_expr w.r.t. param

qfi_method

Returns CircuitQFI.

Returns: CircuitQFI

Return type

CircuitQFI

regularization

Returns the regularization option.

Returns: the regularization option.

Return type

Optional[str]

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